Fibonacci Sequence in trees???

Discussion in 'General Science & Technology' started by Orleander, Aug 27, 2011.

Thread Status:
Not open for further replies.
  1. Orleander OH JOY!!!! Valued Senior Member

    Messages:
    25,817
    Genius kid! One to watch for sure. But how does the Fibonacci Sequence relate to trees? What is this kid seeing? link

    Plenty of us head into the woods to find inspiration. Aidan Dwyer, 13, went to the woods and had a eureka moment that could be a major breakthrough in solar panel design.

    On a bleak winter hiking trip to the Catskill Mountains, the 7th-grader from New York noticed a pattern among tree branches, and determined (as naturalist Charles Bonnet did in 1754) that the pattern represented the Fibonacci sequence of numbers. Aidan wondered why, and figured it had something to do with photosynthesis.

    First he determined the ratios representing the spiral pattern of the leaves and branches on an oak tree, using a cylindrical double-protractor tool of his own design. Then he copied the pattern using a computer program, and built an oak tree-shaped solar array out of PVC pipe. He next built a flat-panel array mounted at 45 degrees, like a typical home rooftop array, and attached data loggers to each model to monitor voltage.

    You can read Aidan’s award-winning essay here, which walks you through his experiment design and his results. But the short story is that his tree design generated much more electricity — especially during the winter solstice, when the sun is at its lowest point in the sky. At that point, the tree design generated 50 percent more power, without any adjustments to its declination angle.

    He determined the tree’s Fibonacci pattern allowed some solar panels to collect sunlight even if others were in shade, and prevented branches on a tree from shading other branches....

    Please Register or Log in to view the hidden image!

     
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. Daedelus Registered Senior Member

    Messages:
    55
    From what I read, it's bogus but hyped up by the media. Sorry, no link. I just Stumbled on it.
     
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. Stoniphi obscurely fossiliferous Valued Senior Member

    Messages:
    3,200
    The Fibonacci Sequence governs the arrangement of leaves on growing plants, among more other things than you can shake a stick at. The pattern of seeds in a sunflower and the shape of chambered sea shells are classic examples of it.

    In a growing plant the pattern maximizes the plants use of sunlight.

    In a flat roof - mounted solar cell array mounted at 45 degrees, there will be only one optimum day a year when the sun is precisely at the right angle (orthogonal) to put a maximal amount of light on the array, this due to the 45 degree critical angle of glass. (At 45 degrees, incident light is 50/50 transmitted/reflected, at 90 degrees 100 % of the light goes into the array) This is why many roof mounted arrays track the sun - to catch as much light as they can for as long as they can. You must remember that the sun comes up in the East and goes down in the West as well as rising and lowering in the sky as the seasons change. If you make an array with the individual cells at various angles, some will get light as others lose it. His looks more artsy than calculated to me, however.

    Please Register or Log in to view the hidden image!



    Gotta congratulate the little fellow for reinventing the wheel though.

    Please Register or Log in to view the hidden image!

     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Randwolf Ignorance killed the cat Valued Senior Member

    Messages:
    4,172
    I always thought this to be true as well, but recently read some contradictory information.
    I don't know for sure which is correct, but I've been spouting this "factoid" to people for decades.

    Many items in nature certainly look pretty magical...

    Please Register or Log in to view the hidden image!




    Please Register or Log in to view the hidden image!




    Please Register or Log in to view the hidden image!

     
  8. Stoniphi obscurely fossiliferous Valued Senior Member

    Messages:
    3,200
    While they are related, there is a difference between the Golden ratio and the Fibonacci Sequence.

    Without going into a deep explanation, it should suffice to say that the Fibonacci Sequence is a series of sums of the natural numbers starting with zero. Each new number is added to the sum of the previous two numbers creating a Series, as:

    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, .... where (0+1=1), (1+1=2), (2+1=3), (3+2=5) etc.

    http://en.wikipedia.org/wiki/Fibonacci_number

    The Golden Ratio (or Golden Mean) comes from a simple 5 pointed star like any child would draw in a picture of the night sky. If you draw that 5 pointed star, it will be 5 triangles with their bases forming a central pentagon. If you consider one of the triangles, the ratio of a side of the triangle to the base of the triangle is ~.62 to 1. If you add those together then the ratio of the sum to the base will be 1.62 to 1 - the Golden Ratio. It is an irrational number, where the decimal part is a non - repeating decimal. The importance of this irrational number was such that the Pythagorans wore the star on their robes to indicate their membership in that secret mathematic society. Irrational numbers were considered sacred and thus secret back then.

    http://en.wikipedia.org/wiki/Golden_ratio

    I have a dear old friend and former mathematics professor who has spent his entire life studying the Fibonacci Sequence and its applications. I have spent a bit of time in that field as well and done many of those constructs, some for money.

    Please Register or Log in to view the hidden image!

    I have not encountered the problems those fellows have with the application of the Fibonacci sequence.

    As for the Golden Ratio...it is formally referred to numerically as "phi", as in "Stoni - Phi"...the concrete instantiation of an irrational number. It is in the same class as "pi" and crops up in interesting places. It is of greater importance to artists than to mathematicians though, at least to my observations.
     
  9. Randwolf Ignorance killed the cat Valued Senior Member

    Messages:
    4,172
    Thank you, Stoniphi, for disambiguating my thoughts.

    Somewhere along the line I had confused the two, thinking Phi was part of a Fibonacci series. Upon reflection, isn't the Golden ratio approximated by the ratio of one Fibonacci number divided by its predecessor? e.g. 34/21 = 1.619, and so on, with each successive iteration becoming closer and closer to the irrational phi?
     
  10. Stoniphi obscurely fossiliferous Valued Senior Member

    Messages:
    3,200
    Yes, it is.

    Please Register or Log in to view the hidden image!

    Part of why mathematics is so very beautiful.

    Symmetry won out in this spacetime, thank dog!

    Please Register or Log in to view the hidden image!



    This leaves me feeling so very....irrational!

    Please Register or Log in to view the hidden image!

     
Thread Status:
Not open for further replies.

Share This Page